On Tuesday night, the Diamondbacks acquired Shelby Miller to upgrade their rotation. The cost of the acquisition, however, led most people — myself included — to conclude that not only did the team pay an exorbitant cost relative to pursuing other options on the market, but that it’s not even clear that the team improved on the field for 2016, given the loss of a quality Major League outfielder in the deal. As has been the case with several other recent moves Arizona has made of late, the reaction to the deal has been extremely negative. But has it been too one-sided and over the top?

Any time the public reaction is this slanted in one direction, it’s reasonable to ask what we we may be missing. We don’t have to ascribe to the idea of perfectly rational actors in every front office to accept the fact that teams have more and better information than we do, and when there’s a big disconnect between what we see and what they see, we should at least consider the possibility that they know more than we do. And when we look back at the recent history of unpopular transactions, there’s a decent amount of evidence that the magnitude of the criticism looks a bit silly in retrospect.

The most obvious comparison to this kind of prospect-for-pitcher trade backlash is the James Shields trade; in the aftermath of that deal, my post about the trade began “Royals Mortgage Future to Be Mediocre in 2013.” And while the Royals did indeed fail to reach the postseason in their first year with Shields, he helped them make a World Series run in 2014, and then they managed to win the whole thing this year, capping off a strong three year run that has revitalized baseball in Kansas City. With the benefit of hindsight, I certainly could have been a bit more nuanced with my opinion on that trade.

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As the reader has certainly heard, the Arizona Diamondbacks sent an impressive collection of talent to Atlanta on Tuesday night in exchange for right-hander Shelby Miller. As Jeff Sullivan has already noted here, the benefits of the deal for the D-backs aren’t particularly easy to identify. They acquire three years of Miller, yes, but at the cost not only of three promising young players, but also of relying more heavily on Yasmany Tomas. In the final analysis, the present gains appear to be minimal, while the future losses are quite possibly substantial.

Among the more notable qualities of the trade is Arizona’s decision to part with shortstop Dansby Swanson, the No. 1 overall pick from the most recent draft. In light of that draft pedigree and his current place among all prospects — MLB.com ranks him 10th currently — it’s not a stretch to suggest that Swanson is worth $50 million right now. Which is to say: a lot. There is, of course, no guarantee that Swanson will be great, but there’s also no guarantee about any of these human people. One works in probabilities, and the probability that Swanson develops into a useful player — or something more impressive than that — is pretty strong.

And here’s the most curious thing: the D-backs just acquired Swanson five months ago. Given a choice of all draft-eligible amateurs back in June, the D-backs selected him. And now they’ve surrendered him less than half a year later. Is it possible that their evaluation of Swanson has changed dramatically over that interval? Yes, but only in the same way that escaping the constant burden of one’s mortality is possible: not very.

And working under the assumption that the D-backs think roughly the same of Swanson that they did back in June, it’s difficult to perform any manner of calculus which suggests that the D-backs have employed maximum wisdom by dealing Swanson et al.

If trading a No. 1 pick a mere five months after his draft seems uncommon, that’s because it is. Indeed, up until this past April, it would have been illegal. That’s when Major League Baseball amended a rule that forbade the trading of a player during the first 12 months following his draft. Now teams must only wait until the conclusion of the World Series. That’s what made Swanson available so soon.

Beyond the rules, however, trading No. 1 picks has been rare anyway. And it follows: a club performs considerable due diligence while leading up to a first-overall selection — and likely becomes attached to the player whom they select. Whether because of their belief in the player, or the considerable investment of time and energy and money which that player represents

So it’s a rare occurrence. But how rare is it?

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With the title of this post, I have given myself an admittedly difficult task, given most comments about this trade since it went down. Arizona traded two top-100 prospects, including one player in the top 25 (at least), as well as a proven major league outfielder in exchange for a somewhat inconsistent pitcher, albeit one coming off a three-win season and with three more years of control. For the most part, everybody is beating up on the Diamondbacks — and for good reason: we don’t know the internal valuations the Diamondbacks possess on their own players and players outside their organization, but there is a general consensus that whatever those valuations are, they do not match up the rest of baseball. As a result, they have undersold their assets compared to the rest of the market. If we take out the external valuations of players like Dansby Swanson, Aaron Blair, and Ender Inciarte, can we make a case that, internally, the decision might have been sound?

What I am trying to get at is this: the trade value on the open market for Dansby Swanson, Aaron Blair, and Ender Inciarte is much greater than one Shelby Miller, but if you are the Diamondbacks and presented one choice and one choice only, how do we get to a spot where you choose Shelby Miller over Dansby Swanson, Aaron Blair, and Ender Inciarte?

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Check out the MLB Trade Rumors page for Justin Upton, and you find something strange. Since a report on November 13 that the outfielder had been extended a qualifying offer, Upton has been invoked just three times there — in one case, with the Angels, merely to note that “nothing is happening” between Upton and the club. Los Angeles was merely engaged in “ongoing conversations” with Upton’s representatives. Whether those conversations are about a possible contract or fondue, no one knows. They’re having conversations.

Now check out the Ben Zobrist page. Even before signing last night with the Cubs, his name was ubiquitous across the site.

And that’s weird. One is 34 and was worth two wins last year. The other is 28 and was worth almost twice as much. You’d think the rumor count would be reversed.

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Just yesterday, we thought the Wade Miley trade might’ve been lopsided. And, you know, maybe. But now we’re on another level. Forget the Wade Miley trade. Now we have the Shelby Miller trade. Kudos to the Diamondbacks — they got Miller, who they wanted. They also got Gabe Speier, who is a player. But Miller didn’t come for free. In exchange, the Braves got Ender Inciarte. Also, the Braves got Dansby Swanson. Also, the Braves got Aaron Blair. Inciarte being a quality, cost-controlled outfielder. Swanson being last year’s first overall pick. Blair being possibly or probably a top-100 starter prospect who’s close to the majors. Don’t get me wrong, Miller is plenty interesting. He ought to help Arizona. Yet the trade looks like a clear, obvious mistake.

You always want to let the first impression settle. You always want to think these things through, to try to make sense from both sides if you can. Sometimes, though, you remain feeling how you initially felt. There’s a parallel you can draw here — the last time I felt like this about a trade, the Royals picked up James Shields. At this point, the Royals don’t regret what they did. There was a way for that to work out for them, just as there’s a way for this to work out for Arizona. But the Shields trade went almost as well for Kansas City as possible. And there’s no Wade Davis in this move. Inciarte might play the part of Wil Myers. Swanson might play the part of Wil Myers. There are two options, with Blair more or less playing the part of Jake Odorizzi. This could easily be a bigger haul, for very probably a lesser return. Occasionally there are bad trades. This is among the worst of them.

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Zack Greinke is one of the best pitchers in major league baseball, and as a result, he had no shortage of suitors before ultimately signing a contract in excess of $200 million. In addition to money, the Diamondbacks also surrendered their first-round pick next year, the 13th overall selection. While it would not be quite true to say that Greinke cost “only money,” the Diamondbacks did not give up a single active player in order to acquire Greinke.

Cole Hamels, both the same age as Greinke and roughly as effective over the course of his career, was traded over the summer. Hamels’ cost was not “only money,” as the Texas Rangers gave up six players, including three high-end prospects (and Matt Harrison’s contract), for Jake Diekman and the opportunity to pay Cole Hamels around $100 million over the next four years. While the costs come in different forms, we can compare the two to see how the trade market this past summer compared to this offseason’s free agent market for Greinke.

The Los Angeles Dodgers prioritized Cole Hamels at the trade deadline, but subsequently missed out by refusing to part with their best prospects. The team then prioritized bringing Greinke back, only to be outbid by division rival Arizona. The cost for both players was high, and it is difficult to say whether the Dodgers made a mistake passing on both players, but we should be able to compare the costs for both to see if the Dodgers could have kept a comparable pitcher for less than the amount Greinke received in free agency.

As far as comparisons go, Greinke did have a better year in 2015, but their cumulative WAR graphs (shown below) reveal two remarkably similar careers in terms of value.

In addition, both players are projected to do well next season. By Steamer, Greinke is set for a 4.2 WAR while Hamels comes in a bit behind at 3.6 WAR for the 2016 season. Using those projections as the baseline for future production, we can get an estimate for their value over the next few years. With deferrals, Greinke’s deal turns out to be $194.5 million over six seasons, per Ken Rosenthal. Given the consistency of both Greinke and Hamels, for the purposes of this analysis, we will assume the players will age well.

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Zack Greinke looks to be worth what the Diamondbacks will be paying him. We still don’t have a complete idea of the structure of his contract, so it’s not like everything can be nailed down precisely, but he’s one of the most valuable pitchers in baseball, and he’s going to get paid like it. When you factor in everything he does — pitch, hit, defend — Greinke’s projected contract comes out looking a lot like his actual contract. So, based on our usual estimates, this is a totally acceptable free-agent deal. Good for Greinke, good for Arizona.

Here’s where it gets more complicated: those usual estimates don’t do much to account for team context. Let’s say the going rate for a win in free agency is $8 million. The specific number doesn’t matter. That’s what any team should expect to pay. But you can’t pay everyone free-agent money — that would mean, to expect 40 team WAR, you’d need a payroll of $320 million. $8 million might be the cost of a win in free agency, for every team, but not every team has the same total $/WAR target. As always, the biggest-spending teams have an advantage. Teams like the Diamondbacks need to be more careful.

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Johnny Cueto didn’t want the Jordan Zimmermann deal with an extra year attached, or so the rumors go. That’s interesting, because the two 29-year-old righties are comparable players:

Johnny Cueto vs Jordan Zimmermann, Since 2011

Name	IP	K%	BB%	xFIP	FIP	ERA
Cueto	889.1	20.7%	6.3%	3.58	3.41	2.71
Zimmermann	971.2	19.8%	4.6%	3.58	3.30	3.14

At least by strikeouts and walks, these two are in the same class. Zimmermann’s strikeout minus walk rate is a little better than Cueto’s, even if the dreadlocked one has a better strikeout rate.

These guys look very similar, until you look at the batted ball stats. Over the last five years, 26.5% of Cueto’s balls in play have been hits, while 29% of Zimmermann’s have been. That’s led to a 2.71 ERA for one and a 3.14 ERA for the other.

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What they may lack in impact bats, the Diamondbacks make up for with pitching depth. They have a lot of pitchers with high floors in the upper levels of the minors, and a few in the low minors that should move quickly. A few have top of the rotation potential. The addition of Dansby Swanson to the organization this June does a lot to help reinforce the offensive pipeline, but the team will have to do a better job developing hitters over the next few years.

Their quantity of outfield options is solid, and was something of a logjam in the upper minors this season. That four players who started playing for the team in 2015 make the top eight here is a good sign for their talent acquisition going forward. Look for the pitchers to start making their presence felt in the big leagues in 2016 and 2017, while we wait on some of the lower-level hitting prospects to put things together.

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No, we aren’t just going to do a leaderboard sort for best movement in each direction and call it a day. It’s a little bit more complicated to figure out the best changeups by shape and speed, mostly because it’s all relative. The changeup, as the name implies, functions off of the fastball, as a change of pace and movement. So we need to define anything the changeup does relative to the pitcher’s fastball.

Then we can do a sort and call it a day.

In order to define fastball movement, let’s just group together all of the fastballs thrown by a pitcher. It’s probably more nuanced than that; the concept of tunneling or sequencing shows that pitchers can pair their changeup with one fastball or the other for different results. But some of this comes out in the wash: by averaging movement across fastballs, their selection of different fastballs will weight the movement in the direction of the pitcher’s usage.

So then our x and y movement, and velocity, are defined against this average fastball for each pitcher. Using a minimum of 50 changeups thrown, and z-scores to sum up the values, we can get a list of best changeups quickly.

First, the relievers.

Best Reliever Changeups by Movement, Velocity

Pitcher	FB (pfx_x)	FB (pfx_z)	FB (velo)	CH (pfx_x)	CH (pfx_y)	CH (velo)	Sum Z	CH swSTR%
Brad Boxberger	-3.3	10.6	92.6	-7.8	2.0	79.8	6.7	14%
Shawn Tolleson	-2.6	11.0	92.9	-4.8	4.0	79.8	4.9	15%
Josh Fields	0.1	11.5	94.1	-0.6	3.7	81.4	4.5	8%
Roberto Osuna	-4.2	10.7	95.5	-8.0	6.9	82.3	4.0	16%
Josh Smith	-4.1	7.6	89.9	-8.4	1.9	79.4	4.0	8%
Chasen Shreve	7.3	10.6	91.4	6.3	1.5	82.6	3.5	18%
A.J. Ramos	-3.0	8.6	92.4	-7.5	1.0	85.5	3.5	35%
Jeff Ferrell	-4.1	10.2	93.0	-7.4	4.9	82.4	3.5	20%
Danny Farquhar	-5.0	8.5	92.7	-7.5	1.0	84.5	3.2	24%
Fernando Rodney	-6.7	7.1	94.7	-9.6	3.3	82.7	3.1	17%
Andrew Schugel	-7.9	7.8	91.6	-9.6	2.3	80.5	3.1	23%
Joaquin Benoit	-6.5	8.9	94.2	-7.5	1.9	84.1	3.1	24%
Tyler Thornburg	-0.8	11.1	92.2	-5.8	6.3	83.8	3.0	19%
Arnold Leon	-5.1	9.8	91.6	-4.6	2.8	80.2	2.9	22%
Pat Neshek	-8.5	4.9	89.9	-4.6	3.7	68.4	2.9	9%
Tommy Kahnle	-1.9	7.4	94.8	-7.6	2.8	87.2	2.8	23%
Mike Morin	-4.7	8.9	92.3	-0.5	6.8	71.7	2.8	25%
Deolis Guerra	-5.1	10.0	90.8	-6.7	4.0	80.7	2.8	15%
Daniel Hudson	-6.6	8.3	96.0	-9.9	4.9	84.8	2.7	18%
Erik Goeddel	-3.9	9.2	93.0	-4.7	2.0	84.3	2.5	32%

SOURCE: PITCHf/x

pfx_x = horizontal movement
pfx_z = vertical movement
Sum Z = sum of the z-scores for the differentials between fastball and changeups in x, y movement and velocity
swSTR% = swinging strikes over pitches for the changeup
Minumum 50 changeups thrown in 2015

If you listen to The Sleeper and The Bust, you know I talk about this all the time and do the math in my head. Now the math is there for us on the sheet of paper.

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